Partition function for the two-dimensional square lattice Ising model in a non-zero magnetic field-A heuristic analysis

TL;DR

This paper presents a heuristic analysis to approximate the partition function of the 2D square lattice Ising model with a non-zero magnetic field, aligning with Onsager's solution when the field is zero.

Contribution

It introduces a heuristic method to estimate the partition function for the 2D Ising model under non-zero magnetic fields, extending Onsager's exact solution.

Findings

Partition function estimates match Onsager's solution at zero magnetic field

Heuristic approach provides approximate solutions for non-zero magnetic fields

Method offers insights into the model's behavior under external magnetic influences

Abstract

The exact partition function of the two-dimensional nearest neighbour Ising model pertaining to square lattices is derived for N sites in the case of a non-vanishing magnetic field.When the magnetic field is zero,the partition functions estimated from the present analysis are identical with those arising from Onsager's exact solution.